mathjs/lib/function/set/setPowerset.js

'use strict';

var flatten = require('../../utils/array').flatten;

function factory (type, config, load, typed) {
  var index = load(require('../../type/matrix/MatrixIndex'));
  var size = load(require('../matrix/size'));
  var subset = load(require('../matrix/subset'));
  var compareNatural = load(require('../relational/compareNatural'));
  
  /**
   * Create the powerset of a (multi)set. (The powerset contains very possible subsets of a (multi)set.)
   * A multi-dimension array will be converted to a single-dimension array before the operation.
   *
   * Syntax:
   *
   *    math.setPowerset(set)
   *
   * Examples:
   *
   *    math.setPowerset([1, 2, 3]);        // returns [[], [1], [2], [3], [1, 2], [1, 3], [2, 3], [1, 2, 3]]
   *
   * See also:
   *
   *    setCartesian
   *
   * @param {Array | Matrix}    a  A (multi)set
   * @return {Array}    The powerset of the (multi)set
   */
  var setPowerset = typed('setPowerset', {
    'Array | Matrix': function (a) {
      if (subset(size(a), new index(0)) === 0) { // if empty, return empty
        return [];
      }
      var b = flatten(Array.isArray(a) ? a : a.toArray()).sort(compareNatural);
      var result = [];
      var number = 0;
      while (number.toString(2).length <= b.length) {
        result.push(_subset(b, number.toString(2).split("").reverse()));
        number++;
      }
      // can not return a matrix, because of the different size of the subarrays
      return _sort(result);
    }
  });

  return setPowerset;
  
  // create subset
  function _subset(array, bitarray) {
    var result = [];
    for (var i=0; i<bitarray.length; i++) {
      if (bitarray[i] === "1") {
        result.push(array[i]);
      }
    }
    return result;
  }
  
  // sort subsests by length
  function _sort(array) {
    var temp = [];
    for (var i=array.length-1; i>0; i--) {
      for (var j=0; j<i; j++) {
        if (array[j].length > array[j+1].length) {
          temp = array[j];
          array[j] = array[j+1];
          array[j+1] = temp;
        }
      }
    }
    return array;
  }
}

exports.name = 'setPowerset';
exports.factory = factory;